Adding and Subtracting Polynomials

Show your work for each problem.

1.
Which terms are like terms?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
and are like terms because both have the variable raised to the power 2. The coefficients (3 and 5) can be different.
2.
Simplify:
Answer: 11x^2
. Add the coefficients, keep the same variable and exponent.
3.
Simplify:
Answer: 5x
. Subtract the coefficients when the operation is subtraction.
4.
What is the result of ?
1. a)
2. b)
3. c)
4. d)
Answer:
5.
Add:
Answer: 4x^2 + 7x
1. Add the terms: 4x^2
2. Add the terms: 7x
3. Write the final answer 4x^2 + 7x
6.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
7.
Simplify:
Answer: 3x^2 + 3x + 4
. We get: for , for , and for constants.
8.
Subtract:
Answer: 3x^2 + 8x - 3
1. Distribute the negative: -x^2 + 3x - 2
2. Combine terms: 3x^2
3. Combine terms: 8x
4. Combine constants: -3
5. Write the final polynomial 3x^2 + 8x - 3
9.
Simplify:
Answer: x^3 + 4x^2 + x + 5
. Write in standard form (descending powers).
10.
Simplify:
Answer: 4x^2 + 8
1. Distribute the negative: -2x^2 + 4x + 5
2. Combine terms: 4x^2
3. Combine terms: 0
4. Combine constants: 8
5. Write the final answer 4x^2 + 8
11.
A rectangle has length and width . If the length is increased by , what is the new length?
1. a)
2. b)
3. c)
4. d)
Answer:
New length
12.
Simplify:
Answer: 4x^2 - 6x + 4
13.
Simplify:
Answer: 2x^3 + 3x^2 + 4x + 1
1. Distribute the negative to the last polynomial: -x^3 + 2x - 1
2. Combine all terms: 2x^3
3. Combine all terms: 3x^2
4. Combine all terms: 4x
5. Combine constants: 1
6. Write the final answer in standard form 2x^3 + 3x^2 + 4x + 1
14.
If and , what is ?
1. a)
2. b)
3. c)
4. d)
Answer:
15.
Find the polynomial that must be added to to get .
Answer: 3x^2 + 6x - 7
1. Set up the equation: . What operation do we need? subtraction
2. Rewrite as subtraction: . Distribute the negative. -2x^2 + 5x - 3
3. Combine terms: 3x^2
4. Combine terms: 6x
5. Combine constants: -7
6. Write the missing polynomial 3x^2 + 6x - 7
16.
Simplify:
Answer: -4x^2 + 8x - 5